Document DOI: 10.1209/epl/i2000-00245-y
Europhys. Lett., 50 (2), p. 135 (2000)
Polycontinuous morphologies and interwoven
helical networks
S. T. Hyde - S. Ramsden
Department of Applied Mathematics,
Research School of Physical Sciences
Australian
National University, Canberra, ACT 0200, Australia
PACS :
02.40.Sf - Manifolds and cell complexes
61.25.Em - Molecular liquids
61.30.Cz - Theory and models of liquid crystal structure
Abstract:
We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, continuous and interwoven sub-volumes. The construction gives helical windings of disjoint graphs on triply periodic hyperbolic surfaces, whose universal cover in the hyperbolic plane consists of packed, parallel trees. The simplest tri-, quadra- and octa-continuous morphologies consist of three (8,3)-c, four (10,3)-a and eight (10,3)-a interwoven networks, respectively. The quadra- and octa-continuous cases are chiral. A novel chiral bicontinuous structure is also derived, closely related to the well-known cubic gyroid mesophase.
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